In the given figure, the two lines AB and CD intersect at a point O such that ∠BOC = 125°.

Question:

In the given figure, the two lines AB and CD intersect at a point O such that ∠BOC = 125°. Find the values of x, y and z.

 

Solution:


Here, ∠AOC and ∠BOC form a linear pair.

∴ ∠AOC + ∠BOC = 180º

⇒ xº + 125º = 180º

⇒ xº = 180º − 125º​ = 55º​

Now, 

∠AOD = ∠BOC = 125º       (Vertically opposite angles)

∴ yº = 125º​

∠BOD = ∠AOC = 55º         (Vertically opposite angles)

∴ zº = 55º​

Thus, the respective values of xy and z are 55, 125 and 55.

 

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